Algebraic motion of vertically displacing plasmas

TL;DR

This paper models the nonlinear vertical motion of tokamak plasmas using an analytical approach that considers the plasma as a rigid body interacting with conducting structures, revealing insights into stability and motion behaviors.

Contribution

It introduces an analytical model capturing the nonlinear vertical plasma motion during displacements, accounting for resistive wall effects and providing a detailed understanding of plasma-wall interactions.

Findings

Resistive wall allows slow drift of equilibrium point.

Initial exponential instability transitions to algebraic sinking.

Plasma acceleration linked to current sharing and quench dynamics.

Abstract

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear "sinking" behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma and the wall or from the thermal quench dynamics precipitating loss of plasma current.